Question: $g(n) = -2n^{2}+5n$ $h(n) = 3n+7-f(n)$ $f(t) = -4t-g(t)$ $ g(h(-1)) = {?} $
First, let's solve for the value of the inner function, $h(-1)$ . Then we'll know what to plug into the outer function. $h(-1) = (3)(-1)+7-f(-1)$ To solve for the value of $h$ , we need to solve for the value of $f(-1)$ $f(-1) = (-4)(-1)-g(-1)$ To solve for the value of $f$ , we need to solve for the value of $g(-1)$ $g(-1) = -2(-1)^{2}+(5)(-1)$ $g(-1) = -7$ That means $f(-1) = (-4)(-1)-(-7)$ $f(-1) = 11$ That means $h(-1) = (3)(-1)+7-11$ $h(-1) = -7$ Now we know that $h(-1) = -7$ . Let's solve for $g(h(-1))$ , which is $g(-7)$ $g(-7) = -2(-7)^{2}+(5)(-7)$ $g(-7) = -133$